In detection of an original recorded signal from a signal reproduced from a storage device, if a reproduced signal includes many non-linear components, it is difficult to remove non-linear components using a conventional linear filter or to transform the reproduced signal into an intended channel form. Particularly, if the non-linearity becomes severe, performance of a system is markedly decreased.
In the case of a magnetic system amongst storage devices (e.g. magnetic system, optical system, optical-magnetic system, etc), a transition shift and a partial erasure occur and thereby non-linear components are increased. Here, a transition refers to a point where positive (+) and negative magnetic components cross, which is used for the signal detection. Thus, the transition shift is also called a bit shift or data dependent position shift. Also, the partial erasure is a phenomenon where the boundary of the left and right of each of the different signals partially collapse.
In the case of an optical system, the non-linear distortion occurs due to astigmation, spherical aberration, coma aberration, and the tilt of a disk, as well as the characteristic of a lens and focal errors.
Meanwhile, in the case of the optical magnetic system, the phenomena of the magnetic system and the optical system occur in combination to produce nonlinear distortion.
Particularly in the magnetic system, even though the influence of the transition shift is removed by the preprocessing, the effect of the partial erasure exists as before, so that it is difficult to equalize the signals using only a linear filter.
In order to equalize the interference between symbols and the non-linear distortion from the signal reproduced from the storage device, the Viterbi algorithm has been suggested. This method is achieved using the trellis transition diagram, so that the signal train can rapidly and easily be restored.
The Viterbi algorithm, simplified to be applicable to a real channel, is called the differential partial response class-IV (PR-IV) Viterbi algorithm. Although this method simplified the PR-IV Viterbi algorithm by the differential metric, the intersymbol interference still cannot be removed completely. Also, since the equalization is performed using a partial response target equalizer (PREQ), the correlation between noise itself and a signal is increased when intending to equalize a channel having a high density (e.g., extended partial response-IV (EPR-IV) to the corresponding PR-IV channel), so that the performance is lowered.
On the other hand, an adaptive PREQ is used in order to cope with a zone bit recording or the change of channel by disc rotation of constant angular velocity. However, since the adaptive PREQ adapts the least mean square (LMS) method even though it is a non-linear channel, much time is consumed in order to find the optimal equalization coefficient. Also, the coefficient is slightly disturbed by the non-linearity and the adaptive white Gaussian noise (AWGN), so the equalization system may be unstable.
Recently, intertrack interference as well as intersymbol interference (ISI) has increased causing undershoot to occur in a channel for the storage device. According to a conventional method, a linear finite impulse response (FIR) filter is adapted in order to remove the undershoot. Or a symbol-by-symbol detector is used for removing the leading undershoot as well as the trailing undershoot.
However, since these methods are based on a tentative decision, coloring of noise occurs if an FIR pole-tip filter is used to remove the leading undershoot. Also, if there is an error in the tentative decision by a tentative detector, capacity of the main Viterbi algorithm detector is deteriorated.
On the other hand, a method for achieving a decision feedback equalizer (DFE) using a feedback RAM instead of a feedback filter has been suggested. Generally, the non-linearity of the storage device is influenced by the previous data, and can nearly be removed by the feedback RAM for processing the ISI of the feedback signal. However, when reading a signal from different track of the storage device, the RAM must be updated with a large amount of data to yield a desired efficiency of reading the signals.
When adapting the feedforward equalizer according to the conventional method, the adaptation to the non-linearity is forcibly required even though it has linear properties, so that additional time is required for obtaining the optimum coefficient. Also, the coefficient converges on an arbitrary value, so it varies more. Also, theoretically the feedforward filter should be capable of changing all ISI, (i.e., linear and non-linear distortion), to the canonical form. However, if the conventional linear LMS method is used, the non-linear error and linear error function as a value for adapting the linear equalizer, so that it is difficult to equalize into the intended channel form.
Meanwhile, if a magnetic channel, in which the ISI is severe and the non-linearity by a postcursor is predominant, is implemented with a DEE using a RAM, the performance thereof is similar to the PR-IV or the EPR-IV, and problems occur related to error propagation and costs required for the implementation. Accordingly, the selection range of the DFE is much less than that of the PR-IV difference metric Viterbi algorithm.